BibTeX
@ARTICLE{
         Hossain2018Pgf,
       crossref = "Christianson2018Sio",
       author = "Shahadat Hossain and Nasrin Hakim Mithila",
       title = "Pattern graph for sparse {H}essian matrix determination",
       journal = "Optimization Methods \& Software",
       volume = "33",
       number = "4--6",
       pages = "1250--1263",
       year = "2018",
       publisher = "Taylor \& Francis",
       doi = "10.1080/10556788.2018.1458849",
       url = "https://doi.org/10.1080/10556788.2018.1458849",
       eprint = "https://doi.org/10.1080/10556788.2018.1458849",
       abstract = "In a recent work, we have proposed the pattern graph as a unifying framework for
         methods that exploit sparsity by matrix compression: row compression, column compression or a
         combination of the two in sparse Jacobian matrix determination. Utilization of structural similarity
         between the matrix and its graph has been found to be beneficial. In this paper, we show that an
         important structural property, symmetry, can be exploited in the formulation of sparse Hessian
         matrix calculations using the pattern graph model. Using the notion of ‘direct
         cover’, we present a new general direct method for the determination of sparse Hessian
         matrices with fixed sparsity pattern and a multicolouring interpretation of it on the pattern graph
         associated with the matrix. A heuristic procedure for finding direct covers is sketched and some
         preliminary numerical test results are provided.",
       booktitle = "Special issue of Optimization Methods \& Software: Advances in
         Algorithmic Differentiation",
       editor = "Bruce Christianson and Shaun A. Forth and Andreas Griewank"
}